Question

Solve the following Trig equation. -3-3sin(theta)=cos^2(theta)

Answer 1

Re-write cos^2 in terms of sin^2 and you have a quadratic!

Answer 2

so i need to solve the LHS?

Answer 3

No. Use the fact cos^2x = 1 - sin^2x, and then move it all to one side and solve as a quadratic

Answer 4

Im not sure how to do that?

Answer 5

I'm using x as theta.

-3-3sinx = cos^2x
=> -3-3sinx = 1-sin^2x
=>sin^2x - 3sin - 4 = 0

Answer 6

Ahh i see how you got it now, now how do i set it up to find on all the solutions from 0<x<2pi?

Answer 7

Just solve it as you would the quadratic y^2 - 3y -4, for sin x.

Note you need solutions -1 <= sin(x) <= 1 , you can ignore the others. arcsin this gives you the first solution

Generally, if you find one solutions 0<x<pi you can find the other as pi-x , and if the solution is -pi<x<0 , you have to add 2pi first before you can find them.

However, in the case of this one (you'll see what I mean) it only gives one solution.

Answer 8

i have to show my work in radians, how do i get the value to use for 2Kpi

Answer 9

wut?

sin^2x -3sinx - 4 = (sin(x) - 4)(sin(x) + 1)

So sin x = ... or ...

However -1 =< sin x =< 1 , so we can ignore one of these.
And then use sin^-1 to work out the values of x.

Answer 10

My questtion says solve each of the following trignometric questions on interval 0<x<2pi, express answers for angles as exact values in radians, I've never done that type of problem like you showed me.

Answer 11

Is the problem that you normally work in degrees, or do you just not know how to find the angle?

Answer 12

i just dont know how to find the angle on this type of problem

Answer 13

Oh, OK. Well can you see what the value of sin(x) is from above?

Answer 14

... I've got to go, so I'll rush this, sorry.

From the factorisation, sin(x) = -1 (we can ignore sin(x) = 4 because it's too big)

We use the inverse sin / arcsin / sin^-1 function

=> arcsin(-1) = -pi/2

But we need a value between 0 and 2pi

20 we can add 2pi => 3/2 pi

this is the only value in the inteval.

Answer 15

Okay thank you for your time!